Inducible Games: Using Tit-for-Tat to Stabilize Outcomes

Assume that one player (A) in a two-person game can probabilistically detect the strategy choice of its opponent (B) in advance, and that this fact is known to both players. We say that A adopts probabilistic tit-for-tat if it credibly commits to cooperating if B does, otherwise not, as signaled by its imperfect detector. In 20 of the 57 distinct 2 ×2 strict ordinal games with no mutually best outcome (35 percent), probabilistic tit-for-tat induces a non-Nash, Pareto-optimal outcome that is favorable to A. We call such games inducible. Sometimes the inducement is “weak,” but more often it is “strong.” As a case study, we consider the current conflict between Israel and Iran over Iran’s possible development of nuclear weapons and show that Israel’s credible commitment to probabilistic tit-for-tat can, with sufficiently accurate intelligence, induce a cooperative choice by Iran in one but not the other of the two plausible games that we argue model this conflict.